Newform orbit 18.16.a.a

• Label: 18.16.a.a
• Level: $18$
• Weight: $16$
• Character orbit: 18.a
• Self dual: yes
• Analytic conductor: $25.685$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$18 = 2 \cdot 3^{2}$
Weight:	$k$	$=$	$16$
Character orbit:	$[\chi]$	$=$	18.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$25.6848309180$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 6)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - 128 * q^2 + 16384 * q^4 - 77646 * q^5 + 762104 * q^7 - 2097152 * q^8 + 9938688 * q^10 - 48011172 * q^11 + 285130118 * q^13 - 97549312 * q^14 + 268435456 * q^16 + 3173671566 * q^17 - 5895116260 * q^19 - 1272152064 * q^20 + 6145430016 * q^22 + 333010392 * q^23 - 24488676809 * q^25 - 36496655104 * q^26 + 12486311936 * q^28 - 117285392310 * q^29 - 225821452768 * q^31 - 34359738368 * q^32 - 406229960448 * q^34 - 59174327184 * q^35 - 477657973906 * q^37 + 754574881280 * q^38 + 162835464192 * q^40 - 1196721561882 * q^41 + 1066802913668 * q^43 - 786615042048 * q^44 - 42625330176 * q^46 - 1324913565264 * q^47 - 4166759003127 * q^49 + 3134550631552 * q^50 + 4671571853312 * q^52 + 6573181204962 * q^53 + 3727875461112 * q^55 - 1598247927808 * q^56 + 15012530215680 * q^58 - 7973946241140 * q^59 + 14311350203222 * q^61 + 28905145954304 * q^62 + 4398046511104 * q^64 - 22139213142228 * q^65 + 41052380998124 * q^67 + 51997434937344 * q^68 + 7574313879552 * q^70 - 67253761134072 * q^71 - 156200366359942 * q^73 + 61140220659968 * q^74 - 96585584803840 * q^76 - 36589506225888 * q^77 - 138004701018640 * q^79 - 20842939416576 * q^80 + 153180359920896 * q^82 - 469396029824988 * q^83 - 246422902413636 * q^85 - 136550772949504 * q^86 + 100686725382144 * q^88 + 422649074576790 * q^89 + 217298803448272 * q^91 + 5456042262528 * q^92 + 169588936353792 * q^94 + 457732197123960 * q^95 - 201862519502686 * q^97 + 533345152400256 * q^98

Embeddings

For each embedding $\iota_m$ of the coefficient field, the values $\iota_m(a_n)$ are shown below.

For more information on an embedded modular form you can click on its label.

Label  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

1.1

0

−128.000

0

16384.0

−77646.0

0

762104.

−2.09715e6

0

9.93869e6

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$3$	$-1$

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	18.16.a.a		1
3.b	odd	2	1		6.16.a.c	✓	1
4.b	odd	2	1		144.16.a.e		1
12.b	even	2	1		48.16.a.b		1
15.d	odd	2	1		150.16.a.a		1
15.e	even	4	2		150.16.c.h		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
6.16.a.c	✓	1	3.b	odd	2	1
18.16.a.a		1	1.a	even	1	1	trivial
48.16.a.b		1	12.b	even	2	1
144.16.a.e		1	4.b	odd	2	1
150.16.a.a		1	15.d	odd	2	1
150.16.c.h		2	15.e	even	4	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{5} + 77646$ acting on $S_{16}^{\mathrm{new}}(\Gamma_0(18))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 128$
$3$	$T$
$5$	$T + 77646$
$7$	$T - 762104$
$11$	$T + 48011172$